Rovelli 5: Fundamental Constants of the Universe

This is my fifth post on Carlo Rovelli's new book, Reality Is Not What It Seems. The first three posts were:

• From Democritus to Relativity to Quantum Mechanics
• Spacetime is Quantum
• Quanta of Space
• Time Does Not Exist

1. Chapters 8-11 are fairly short. Some of it covers basic material from cosmology but there are some helpful synthetic thoughts too.

Chapter 8 fills in some gaps with regard to the Big Bang. He gives high praise to Georges Lemaître, a Belgian priest, for supporting the idea of a "primordial atom" even though Einstein strongly disagreed. Einstein's equations seemed to suggest that the universe was expanding, but he didn't want to believe it. In fact he added a "cosmological constant" to his equations to fix it (Λ). Lemaître turned out to be right about expansion.

Then Einstein lamented adding the cosmological constant and wanted to remove it. Again, Lemaître suggested he should leave it. Lemaître proved to be right again over Einstein. So in both cases Rovelli writes, "It doesn't fall to everyone to disprove Einstein" (204).

Then Lemaître stopped the Pope, apparently, from making the Big Bang official church belief. Again Rovelli says, "It is not given to everyone to disprove the pope" (205). This falls under the principle of not inserting God too dogmatically into your scientific theories, because theories change.

2. Rovelli favors something he calls "the Big Bounce." The idea here is that "our universe could be the collapse of a previous contracting universe passing across a quantum phase, where space and time are dissolved into probabilities" (208). This seems to me to be a form of the oscillating Big Bang theory.

I thought that the current sense of things was that there was not enough matter in the universe to pull everything back together and thus that the universe was headed for a "Big Rip" at the end of things. This is also different from the multiverse idea that other books I've read have suggested, namely, that our universe is just one of an infinite number of universe bubbles.

Meanwhile, Rovelli nicely, I think, counters Lee Smolin's sense that the universe is all there is by definition. Rovelli, much more soundly says, "The word 'universe' has assumed another meaning in cosmology: it refers to the spacetime continuum that we see directly around us, filled with galaxies and history of which we observe. There is no reason to be certain that, in this sense, this universe is the only one in existence" (208).

Take that Smolin, who says in the first chapter of Quantum Gravity, "By definition the universe is all there is" (17). Let's just say Rovelli is a much better philosopher, although I don't always agree with him.

The dissolution of spacetime into a cloud of possibilities when you have that much mass at a quantum size is an intriguing idea.

3. Chapter 9 asks if we have any experimental evidence for loop quantum gravity. A number of times he pushes back both against those who say you cannot talk about anything that you cannot now experimentally show and those who wildly speculate detached from current trajectories. To me this positioning makes perfect sense.

On the one hand, a theory should proceed to experimentation. "A theory lacking empirical confirmation is a theory that has not yet passed its exams" (212). On the other hand, he disagrees with wild hypotheses. "Many theoretical physicists are today looking for new theories by picking arbitrary hypotheses... I don't think that this way of doing science has ever produced good results" (215-16).

Rather, all the experimental evidence has been confirming the three cornerstones of modern physics: general relativity, quantum mechanics, and the Standard Model within quantum mechanics. The new findings have brought a complete absence of surprise. Hawking was disappointed.

The three big findings of this decade are 1) the confirmation of the Higgs boson, 2) the cosmic measurements of the Planck satellite, and 3) the detection of gravitational waves.

Also, the fact that CERN has not discovered supersymmetry is a blow to string theorists, which is why Sheldon on Big Bang Theory went looking for something else to study. :-)

4. Mapping of the cosmos has given us a sense of the lay of the background radiation left not too long after the so called Big Bang. The idea here is that it took some time for the universe to cool down enough for the light (photons) of creation to be released.

The remnants of this release are called "cosmic background radiation" (CBR), alleged to have happened some 380,000 years after the Big Bang.

Apparently, if LQG is correct (loop quantum gravity), then there should also be a gravitational background radiation. An experiment called LISA involving three satellites around the sun, might be able to test for these.

5. Chapter 10 looks at quantum black holes. There are black holes at the centers of most galaxies and, in at least one theory, they may account for what it otherwise called dark matter.

The horizon of a black hole is the point where you might stay out. Past that, nothing can get out. Time stops at the horizon. Stephen Hawking's claim to fame was his discovery that black holes slowly evaporate. Eugenio Bianchi showed that loop quantum gravity can also demonstrate Hawking's formula for the heat of a black hole.

What LQG would show is that, since spacetime is not infinitely divisible--since it never can reach a singularity--at some point a black hole should explode in a miniature version of the Big Bang. From our perspective outside a black hole, this would take billions years, even if it is only moments inside the black hole. Since the universe is allegedly 14 billion years old, we might find some of these. Rovelli suggests that some "fast radio bursts" detected by radio telescopes could be such.

6. Chapter 11 is called the end of infinity. The common sense of the suggestion here is so obvious I've thought of it for some time now and I'm not even a scientist. Why didn't Dirac and Feynman? Quantum mechanics and relativity are plagued with infinities. Feynman the pragmatist simply substituted the experimental values for certain infinities to get his equations to work.

But LQG, because it sees space as quantized, eliminates the infinities. This seems so obvious to me that it is surprising it is not a fundamental working assumption of modern physics.

"Putting a limit to infinity is a recurrent theme in modern physics. Special relativity may be summarized as the discovery that there exists a maximum velocity for all physical systems. Quantum mechanics can be summarized as the discovery that there exists a maximum of information for each physical system. The minimum length is the Planck length L_P, the maximum velocity is the speed of light c, and the total information is determined by the Planck constant h" (232).

Now we are getting somewhere. This is what I've been thinking and looking for someone to put succinctly like this. "The existence of these minimum and maximum values for length, velocity, and action fixes a natural system of units. Instead of measuring speed in kilometers per hour... we can measure it in fractions of the speed of light.. In the same way, we can posit L_P = 1 by definition and measure length in multiples of Planck's length. And we can posit h = 1 and measure actions in multiples of Planck's constant. In this way, we have a natural system of fundamental unities from which the others follow" (233).

One more seems to complete Rovelli's set, namely, the cosmological constant (Λ) used in relativity. I have a book called Just Six Numbers that is also on my reading list. I'm hoping it will help me understand the importance of the ratio between the cosmological constant and the Planck length.

My next post should finish the book.

Rovelli 4: Time Does Not Exist

This is my fourth post on Carlo Rovelli's new book, Reality Is Not What It Seems. The first three posts were:

• From Democritus to Relativity to Quantum Mechanics
• Spacetime is Quantum
• Quanta of Space

1. Chapter 7 is getting closer to theology. I have always been sympathetic to the medieval view that God is outside time. God immanent goes through time with us. God transcendent sees all of time in an eternal now. This construct provides a helpful way around the "Does omniscience imply determinism" debate.

I had the thought while reading this chapter, "God is quantumly entangled with the entirety of his creation." Quantum entanglement is the sense that when two paired particles go their separate way, their states remain connected. In Quantum Gravity, Smolin suggests that this connection can apply to particles inside and outside a black hole.

So I was playfully musing of God knowing every quanta of the universe from its connectness with him at the moment of creation. It's not a suggestion or completely satisfying. After all, this musing does not clearly relate to the future. It would only suggest an exhaustive knowledge of the present and the past.

2. One of the implications of general relativity is that "every object has its own time, running at a pace determined by the local gravitational field" (178). If I am traveling close to the speed of light and you are not, I will age much slower than you will. If you live on a planet with a much greater gravitational field than earth, you will age more slowly than me back on earth. In fact, someone who spends their whole life in Tibet will be a fraction of a second older than me, living my whole life at the Dead Sea, even if we were born at the same exact moment somewhere.

"Time" does not pass at the same rate everywhere.

One thing Rovelli has already mentioned is that, in some of the fundamental quantum gravity equations (e.g., Wheeler-DeWitt), there is no time variable. How is that possible? It gets back to a principle he has stated in his chapter on quantum mechanics. Reality is relational.

Quanta of gravity do not change "in time." Time is simply a counting of the interactions of quanta of gravity. The world is not something that changes "in time," for time does not exist. There is only process after process. "There is no longer space that 'contains' the world, and no longer time 'during the course of which' events occur" (183).

I am hoping I will have a better sense of what I am saying by the end of the book. :-)

3. So an event does not take place in spacetime. Rather, spacetime is part of the event. The event is a process with an initial and final state. And there is a boundary for the event.

"If quantum space has the structure of a spin network, what structure will spacetime have?" (186). Spacetime is the history of a spin network. This history of a spin network is apparently what Loop Quantum Gravity (LQG) physicists call "spinfoam."

I don't really like this word. The idea seems to be that the area of the node foams up to the beach of the line between nodes. And that beach is a spin line. I'm sure I'm massacring it.

"To compute the probability of a process, one must sum up over all the possible spinfoams within the box that have the same boundary in the process. The boundary of a spinfoam is a spin network and the matter on it" (187). This is what Feynman did to calculate the probability of a particle's trajectory.

4. So to sum up the chapter. "Space is a spin network whose nodes represent its elementary grains [of gravity], and whose links describe their proximity relations" (192). What we call spacetime is the transformation of these spin networks into and apart from one another, and the history of these spin networks is called "spinfoam."

So all reality is variations on quantum fields, fields one on top of the other. Another name for these are "covariant" quantum fields. These are, in Rovelli's mind, the fundamental reality that connects spacetime with quantum fields.

More to come...

Rovelli 3: Quanta of Space

This is my third post on Carlo Rovelli's new book, Reality Is Not What It Seems. The first two posts were:

• From Democritus to Relativity to Quantum Mechanics
• Spacetime is Quantum

1. This chapter is not long but it is getting at the things I am interested in right now. I re-skimed chapter 10 of Lee Smolin's Three Roads to Quantum Gravity to cross-reference their material. That chapter is called "Knots, Links, and Kinks." I see Smolin's coming out with a new edition.

Because I don't know the math, because they don't fully give the math, it's hard to get more than just an impression from these chapters. But I like the basic theses.

2. We already have the first key truth. Both space and time reduce to quanta. Space is not infinitesimally continuous. Time is not infinitesimally continuous. I like it.

Now here's another biggie. Gravity reduces to quanta, discrete units of gravity. The quanta of gravity are not in space. "They are themselves space" (172). "Quanta of gravity constitute space itself."

Using another picture, space reduces to discrete packets of volume, which we might call "nodes." "Volume is a property of the gravitational field, expressing 'how much gravitational field' there is" (163-64). The imaginary lines between these nodes are called "links," and a whole set of such intersecting lines is called a "graph."

Nodes, Links, and Graph (Rovelli)

3. There is an area associated with the lines between nodes, which is roughly the square of the Planck length mentioned in the previous post (8πL² times the square root of the spin times one plus the spin, with the spin coming in half integers). When we think of a larger three dimensional volume, the volume is the sum of the volumes of the nodes. Such a volume is a "spin network."

4. After writing all that, there is a danger of thinking that these nodes are space. But Rovelli and Smolin would both want to clarify that, like the electron, it is in the interaction of these gravitational quanta that space exists. Space is not in the node nor is the node space. Space is what happens when the nodes interact, if I understand correctly.

Rovelli 2: Spacetime is Quantum

This is my second post on Carlo Rovelli's new book, Reality Is Not What It Seems. The first post was:

• From Democritus to Relativity to Quantum Mechanics

1. My book has now been baptized in coffee, but is still readable. I suppose it was inevitable.

We now hit the problem edge of physics in chapter 5. Quantum mechanics works for things that are very small. General relativity works for things that are very big. They contradict each other.

Relativity says that spacetime is curved and continuous. Quantum mechanics says that space is flat and energy is discontinuous.

This contradiction is not a problem unless you are dealing with something that is both very small and yet has tremendous mass. In other words, black holes and the Big Bang.

2. A favorite scientist of Rovelli is clearly the Russian, Matvei Bronštejn, put to death under Stalin in 1938. He apparently suggested before his death that, following Heisenberg's uncertainty principle, the narrowness of location would require great ambiguity in momentum. The energy this would involve at a particular point would be so great as to create a black hole.

The bottom line, Bronštejn suggested that this thought experiment implied a limit to the divisibility of space. The minimum space is around:

This "Planck length" combines the three fundamental constants of nature. "H bar," as it is called, is fundamental to quantum mechanics. C is the speed of light from special relativity. And G is the gravitational constant from general relativity.

3. The next turn in the chapter is to John Wheeler, who coined the phrase black hole. It was not too long ago that many physicists were skeptical about their existence, but now it is overwhelmingly accepted.

Apparently, Wheeler and Bryce DeWitt come up with an equation for the "foaming" of space at the Planck level, the "Wheeler-DeWitt equation." Here I am beyond much acquaintance. What is most curious about the equation is that it does not have a time variable. How do you describe interactions on the most fundamental level of reality without a time component?

There will me more to come on this subject. I have some other sources that I may use to try to triangulate.

4. We are close to the birth of quantum loop gravity, the main contender with string theory for ultimate reality right now. In the late 80s, Abhay Ashtekar simplifies and rewrites the Wheeler-DeWitt equation. Lee Smolin tells the same story from his perspective in Three Roads to Quantum Gravity.

Smolin and a guy named Ted Jacobson find some solutions to this equation. The equation only has solutions when lines "loop" in space. Thus "loop quantum gravity" is born.

More to come...